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Chapter Five
Attempting Objectivity
5.1 Introduction – Roger Marsh
It is now necessary to try to bring some objectivity to the assessment of the
correspondence between learning strategy and audible results. In the last chapter
the use of a waveform editor was mentioned (in note 4) when trying to analyse
how two performers approached a problematic bar of Ferneyhough’s Kurze
Schatten II. In this chapter this method is extended and applied to several
recordings to see if useful information can be gained by comparative analysis, as
opposed to the examination of isolated instances. One obvious difficulty here is the
paucity of recorded versions for comparison.
Analysing music in this way is problematic so a fairly thorough discussion will be
given of the limitations of such analyses. There is also the question of how
objective this process can be. Whilst a recording, even of a live performance, is a
fixed entity, performers, understandably, do not try to recreate exact performances
time after time. On the other hand, one might presume that a commercially
available recording represents a performer’s considered view of the piece, albeit at
a particular time. It may even come with an endorsement from the composer. It is
however, unrealistic to analyse more than a few bars from some representative
pieces played by several performers on different instruments. It is also
unnecessary. If the few bars chosen show some characteristics with regard to
rhythmic interpretation it would be absurd to assume the other bars of the piece
are miraculously free of any such deviations.
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In Heroic Motives. Roger Marsh Considers the Relation between Sign and Sound in
‘Complex’ Music (Marsh 1994), Marsh considered this question of rhythmic
accuracy with an analysis of several bars of Irvine Arditti’s performance of
Ferneyhough’s INTERMEDIO alla ciaccona and the Arditti String Quartet’s
recording of Ferneyhough’s Second String Quartet1. Marsh did not give details of
the methods or instruments he used to calculate the durations he gives apart from
the use of a calculator, but one might speculate the use of a stopwatch as durations
of one thousandth of a second are given. With the wide availability of waveform
editors, very precise measurements are now possible. Marsh’s example, and
several others, will be reconsidered here and an alternative analysis of Arditti’s
interpretation, using the waveform editor Audacity (1.3), will be given.
Interpreting the results of such analyses is far from simple as it involves the nature
and meaning of measurement, the philosophical difficulties concerning the nature
of a score, interpretation of composer-‐specific requirements and expectations, the
meaning of meter and rhythm, and the natural instinct of a performer to ‘interpret’
and to some extent inject their own personality or individuality into the music. Any
comments that follow are in no way to be interpreted as critical of any of the
performances, the pieces or the composers, and whilst Ferneyhough’s music
quintessentially exhibits the most extreme rhythmic complexities, and has been
chosen for analysis for that reason, the music of other composers writing in this
genre could equally well have been chosen.
It is also important to be absolutely clear about what is being measured. Recalling
Ferneyhough’s comment quoted in Chapter Four, that no interpretation should be
an exact reflection of the notation and ‘nor should it be’, it is quite obvious that the
larger musical structures should not be the focus of attention. What is at issue is
the performance of the precisely notated rhythmic details and placement of the
rhythmic figure within its metrical context. Examples were given in Chapter Four.
These are the details that some performers claim they calculate minutely.
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Once information about such rhythmic accuracy has been determined, then should
there be perceived inaccuracies, it is possible to speculate on the reasons why this
is the case. These might include instrumentally specific demands, the performer’s
consideration of the other features of the score at that point, matters of phrasing,
gesture and generally what might be considered interpretation. For each of the
following examples these issues will be considered, after the data has been given,
in a separate section. This study is therefore a direct ‘updating’ of Marsh’s work
with his same criteria.
When considering what excerpts to examine it is important that the pulse be slow
enough for the perception of the detail2. Most of the examples that have been
chosen have metronome marks less than 60. There are other factors that
determine the suitability of an excerpt for analysis. The following examples were
chosen so that the accuracy of the performance of the rhythmic figuration could be
determined. There must be no obvious indication that the composer intended
some rhythmic licence. Indeed, most of the examples have some indication from
the composer that their intention is some form of tempo giusto. If a performer were
to impose a degree of rubato on the excerpt then the responsibility must weigh
with that performer. There are clearly passages in new complexity compositions
where the composer intends some rhythmic flexibility (via, for example, explicit
phrasing or prescriptive writing) and two of the examples given can be considered
to fall in to that category. If it is clear that the composer did not intend complete
rhythmic accuracy the excerpt is obviously not suitable for the analytic methods
used here. Where phrasing is understood and clearly the intention of the composer
(for example in Williams’s recording of the bourrée) the bars signifying rhythmic
distortion because of the phrasing were discarded for the purposes of analysis so
that information about the rhythmic accuracy in the other bars could be
ascertained.
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5.2 Measurement; methods and criteria – Ferneyhough’s Kurze Schatten II
This first example (Example 5.1), bars 13 and 14 from Ferneyhough’s Kurze
Schatten II for guitar, was discussed in the previous chapter (section 4.1) where
the question was raised of the ambiguity of the placing of the last note in the top
voice in bar 14. The speculation was made that the 31:24 subdivision was an error
due to the absence of an 8th note rest. The recordings by Magnus Andersson and
Geoffrey Morris were compared to elicit their solutions to this problem (chapter
Four, footnote 4). Of course another explanation could be that the subdivision
should be 27:24 and, faut de mieux, the analysis will use this.
Example 5.1 Ferneyhough, Kurze Schatten II, 1st movement, bars 13-‐14
This example serves as a useful introduction to all the problems described above
and will therefore be considered in more detail than the examples that follow.
Example 5.2 is a schematic representation of Example 5.1. If accuracy of rhythm is
the main purpose of this analysis then it is clear that not every one of the 26 notes
that are to be played in these two bars needs to be assessed, for if a certain number
of significant notes are evaluated the others will be relatively correct or incorrect
by association. That is, if these significant notes are reasonably accurately placed
then further investigation of the remaining notes might be considered desirable for
a more detailed view. If the significant notes are inaccurately placed (according to
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some criteria) then investigation of the remaining notes is pointless. The numbers
in Example 5.2 therefore refer to the notes that were measured. Here the word
‘measured’ refers to the assessment of the placement of the note on the wave
editor.
Example 5.2 Ferneyhough, Kurze Schatten II, 1st movement, bars 13-‐14 –
schematic with significant notes
All the struck notes in the top two voices are measured but in the lower voice only
the first notes of each of the note groupings are measured. The following table,
Table 5.1, shows the placements of the 15 notes chosen for measurement from the
recording in flagranti by Geoffrey Morris (Morris 2000) (who has recorded the
piece twice3). The measurement is in minutes and seconds to two decimal places4.
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Table 5.1 Ferneyhough, Kurze Schatten II, 1st movement, bars 13-‐14 – actual
timings of significant notes
Significant notes Actual time (secs) 1 1: 19.20 2 1: 20.03 3 1: 20.75 4 1: 21.47 5 1: 22.72 6 1: 23.58 7 1: 24.12 8 1: 24.85 9 1: 25.45 10 1: 26.22 11 1: 27.00 12 1: 27.93 13 1: 28.72 14 1: 29.79 15 1: 30.47
Whilst Ferneyhough gives a metronome marking of 8th note = ca. 44 it is only
possible to make sense of these timings if the exact tempo that Morris uses is
determined. Also it cannot be assumed that the metronome marking used in bar 13
will be the same in bar 14. As a note is played at the beginning of each bar it is easy
to calculate the duration of bar 13 and hence derive a metric. Notes 1 and 10 (the
starting timings of bars 13 and 14 respectively) are 7.2 seconds apart and hence
each of the seven 16th notes should take 1.002857143 seconds. This corresponds
to a metronome marking of 16th = 59.982905982 or 8th = 29.91452991. This is
substantially slower than Ferneyhough’s suggested tempo, even taking the ‘circa’
into account. The first measurement problem is now obvious. The calculator can
manipulate figures to nine decimal places but for practical purposes it is
unrealistic to expect subdivisions of thousandths of a second from a performer.
Therefore a rounding of figures such as these to no more than three decimal places
(and more often two) will be given. Still, small errors can accumulate and it will not
be surprising if expected values are different by small margins of this magnitude.
Given also that most digital metronomes now increment in units of one and not
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fractions, it seems reasonable to assume that should a performer use a metronome
at all, they use commercially available ones with such a limitation. It is of course
quite possible that some performers have access to ever more accurate
metronomes. Given this it seems reasonable to assume that Morris’s tempo is 16th
= 60 – i.e. one 16th note = 1 second and the third column of the following table,
Table 5.2 shows where the fifteen notes should come using this metronome mark
(colour coded for each bar).
Table 5.2 Ferneyhough, Kurze Schatten II, 1st movement, bars 13-‐14 – actual and
theoretical timings of significant notes
Here it is assumed that this metronome mark has continued in to bar 14. It is less
easy to calculate the length of bar 14 as the first note of bar 15 is played five 22nds
(of the bar’s length) from the start of the bar (Example 5.3, bar 15).
Note Actual timing (min:secs)
Theoretical timing
(min:secs)
Difference (minus
means late)
Comments
1 1: 19.20 1: 19.20 0 by construction
2 1: 20.03 1: 19.597 -‐0.433
3 1: 20.75 1: 20.948 0.198
4 1: 21.47 1: 20.988 -‐0.482
5 1: 22.72 1: 23.372 0.652
6 1: 23.58 1: 24.356 0.776
7 1: 24.12 1: 25.036 0.916
8 1: 24.85 1: 25.16 0.31
9 1: 25.45 1: 25.607 0.157
10 1: 26.22 1: 26.22 0 by construction
11 1: 27.00 1: 26.91 -‐0.09
12 1: 27.93 1: 27.109 -‐0.821
13 1: 28.72 1: 27.12 -‐1.60
14 1: 29.79 1: 27.42 -‐2.37
15 1: 30.47 1: 28 -‐2.47
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Example 5.3 Ferneyhough, Kurze Schatten II, 1st movement, bars 15-‐16
Bar 16 starts at 1:43.92 (that is, one minute, 43.92 seconds – this standard format
for the representation of time will be used from now on). The first note played in
bar 15, a bar in 19/16 subdivided into twenty-‐two 16th notes, comes on the fifth
16th note at 1:37.6. It follows by simple arithmetic that the remaining eighteen 16th
notes last for 6.32 seconds and the first quarter note should therefore have a
duration of 1.404 seconds that then implies bar 15 starts at 1:36.196. Bar 14 can
now be assessed as lasting for 9.98 seconds: the 8th note now has a duration of
1.663 seconds and the 16th note = 0.832 seconds (as opposed to 1.002857143).
Whilst the 16th note duration may not seem substantially slower than in bar 13, the
8th note is 0.343 of a second slower5.
This is an illustration of one of the problems of calculating a metric. It is not
possible to know where Morris places the bar line when there is no ictus. It is not
possible to differentiate sustained notes or silences either side of a bar line. As an
aside, Gordon Downie’s Piano Piece 26 contains not one bar (in 51 pages) that
doesn’t start or end with rests or tied notes (see for instance Example 5.4).
Calculating metrics for this piece is a much more laborious process.
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Example 5.4. Downie, Piano Piece 2, page 11
8th = 50
One reason why the performer may change tempo slightly between bars is the not
uncommon practice of learning the pieces bar by bar (see for example (Schick
1994, 136)). The resulting performance may retain elements of this learning
process.
The fourth column of Table 5.2 shows the differences in seconds between the
actual and theoretical timings a tempo (inferred on the basis of the bar length). No
information about rhythmic accuracy can be obtained from the timings of notes 1
and 10, as they are the notes that have been chosen to calculate the others. Looking
at bar 13, the variation in the notes 2 to 9 is quite considerable – three of the notes
coming over half a second early. Notes 4 and 5 are consecutive (schematically) in
the lower part and should be 23.372 – 20.988 = 2.384 seconds apart. They are
played at 22.72 – 21.47 = 1.25 seconds distant – a discrepancy of 1.134 seconds
over four 16th notes duration. Ever larger discrepancies occur in bar 14. Geoffrey
Morris has written (Morris 2002, 16) that he uses a calculator to ‘establish the
changing tempos of sections’ and he uses a pre-‐programmable metronome with a
foot pedal that can store 20 different speeds. This cannot be doubted but whether
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the learning process becomes a part of the final performance is another question.
Other reasons for the variance of the rhythm will be discussed later.
The next question is: what rhythmic accuracy might we expect? We expect a
degree of instrumental precision but also a flexibility of interpretation from the
performer. That the ear can discriminate events of thousandths of a second apart is
accepted but this is not the same as the ability to sense such small time intervals in
the context of aesthetic appreciation of the flow of music7. For example, most
teachers will expect their students to be able to discriminate between the rhythm
of dotted 8th followed by a 16th note and a 2/3rd, 1/3rd of a triplet subdivision. At a
quarter note = 60 (the tempo of the 16th note in bar 13 above) the difference
between the two would be 0.09 second. These rhythms are well known however
and come nowhere near close to the rhythmic complexities encountered in
Ferneyhough’s music. On the other hand it is possible to subdivide bar 13 into
seven 16th note intervals and calculate the closeness to these beats as acciaccaturas
of different degrees of separation. This is essentially Steve Schick’s third method as
described in the previous chapter. This method would at least make meter the
primary consideration and seems to accord with Ferneyhough’s views on its
importance (Schick 1994, 138).
Another area of concern is the measurement of note placements using a waveform
editor. Of course the music is audible and can be played back at any speed whilst
viewing the waveform so the ear can, and must, be part of the judgement. The
problem is that at ever-‐greater resolutions the waveform becomes more difficult to
determine. This is different for different instruments. For example percussion
instruments, particularly woodblocks or high, non-‐pitched sounds have a very
clear waveform. It is almost impossible to determine accurately the initial stroke of
a violin bow. Some notes played very quietly may not register significantly even
when the amplitude axis is ‘stretched’. Several notes played simultaneously or in
very quick succession may be difficult to separate.
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The following screen shots of the waveforms of Example 5.1 give some indication
of the nature of the difficulties. Notes played on the guitar are fairly easy to
determine on the waveform unless they are extremely soft. Example 5.5 shows a
low resolution from about 1:15 to 1:48 so includes bars 13, 14 and 15. The four
piano notes at the start of bar 14 at 1:26.22 seconds are not at all distinguishable.
The x-‐axis represents time. The y-‐axis, representing volume (amplitude), is
measured in decibels (dB) and is the default of the editor.
Example 5.5 Ferneyhough, Kurze Schatten II, 1st movement – waveform from 1:15
to 1:48 including bars 13-‐15
Example 5.6 shows a higher resolution that starts at 1:19 continuing to 1:27, a little
in to bar 15. The amplitude axis has been stretched to fill the pane but the same
four piano notes at the start of bar 14 (1:26.22) are still all but indistinguishable.
The ‘loop play’ function in Audacity is extremely useful in determining the placing
of these notes. Whilst the higher resolution is essential if ever more accurate
timings are desired, watching the progress of the music in real time at this or
higher resolution is difficult as it zips by so quickly. Hand-‐eye coordination to
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pause or start the program at certain points determined by the ear became a useful
skill, the keyboard short cuts proving more efficient than the computer mouse.
Example 5.6 Ferneyhough, Kurze Schatten II, 1st movement – waveform from
1:19 to 1:27
Example 5.7 shows an even higher resolution from 1:23.2 to 1:27 – roughly
covering notes 6 to 11 and again the amplitude axis is stretched to maximum.
Although the score shows that nine notes are to be struck in this period it is
impossible to distinguish them by looking at the waveform. It is a useful tool but
the ear is still essential to discriminate quieter notes. Higher resolutions are
possible but with similar problems. It is likely that greater familiarity with the
program Audacity could result in a more detailed and accurate analysis.
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Example 5.7 Ferneyhough, Kurze Schatten II, 1st movement – waveform from
1:23.2 to 1:27
Finally, there is the issue of errors of calculation when so many numbers are being
manipulated, even with the help of a calculator.
These issues will only be mentioned in passing from now on.
5.3 Graphical representation of results
Footnote 4 states the use of graphical representation as a primary means of
illustrating faithfully the information given in the above tables was rejected. Whilst
the notion is superficially attractive it might be helpful to give some examples of
problems encountered when trying to produce accurate representations of the
data. These problems are analogous to those encountered above in the analysis of
the waveforms.
In detail: to represent differences of 100ths of a second (the time intervals most
commonly used in the tables) the divisions on the coordinate axes must be
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commensurate. Each second will therefore need to be represented by one hundred
units. For a scale of 1mm = 100th of a second (about the smallest subdivision that is
visibly distinguishable on paper), a duration of one second will be represented by a
line 10 cm long. Example 5.1 is about 12 seconds long so the line needs to be 120
cm long – i.e. 1.2m. This will represent the numbered ‘significant’ notes 1-‐15 but
the line would need to be 1.7 m long to represent the complete two bar excerpt.
Strictly speaking coordinate axes at right angles, each representing the time
elapsing, would require a similar area of paper. Reducing the scale to 1mm = 10th
of a second results in a graph that shows the theoretical/actual times to be visually
identical and therefore deceptive. It also follows that while the graph may be full
size, reducing it to fit on an A4 page will cause a similar diminishing of
representational detail.
The use of one axis to simply represent the numbered notes would not indicate the
time durations between these notes so would be unsatisfactory. There would still
be the problem of representing the actual times.
Other representations are of course possible; for example, note number against
time differences between theoretical and actual time. In Table 5.2, this would be
column 1 plotted against column 4. These representations do not illuminate the
research findings.
This thesis is about the assessment of rhythmic accuracy. This entails the
measurement of very small time differences and engaging with the numbers if the
information is to be understood. A glance at a pictorial representation of the data
will not help, or be sufficient, to absorb any of the information. It may well be
deceptive. However, the summary after each table indicates the important points.
It is of course possible to represent the information graphically in a less accurate
format. This will be given later with the strong advice that interpretation of this be
treated with caution and that the information provided in the tables will be more
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accurate.
5.4 John Williams’s recording of Bourrée 1 from Cello Suite BWV 1009 (J.S.Bach)
A rigorous, scientific approach to analysis often necessitates the need for a control,
that is, a parallel investigation or analysis where the variable, or that which is
being assessed (in this case rhythmic accuracy), is held constant – or, as in this
case, is uncontroversial. A metronome is a possibility but as it is a surrogate clock –
and hence essentially the instrument we are using to analyse these examples – and
as the human element would appear to be what we wish to measure, it is not
acceptable. The choice has been made to use John Williams’s recording of the first
eight bars of the Bourrée 1 from the J S Bach’s Cello Suite, BWV 10098. The music is
highly rhythmic, with a simple structure and measurement of note placements is
relatively easy to determine.
Example 5.8 shows these eight bars9 and Example 5.9 is a schematic
representation with the significant notes that have been chosen for measurement.
Example 5.8 Bach, Cello Suite BWV 1009 – Bourrée 1, bars 1-‐8
(The fingering in this example is by John Williams and John Duarte.)
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Example 5.9 Bach, Cello Suite BWV 1009 – Bourrée 1 – schematic of bars 1-‐8
The problem with analysing this example (and most similar examples) is that
phrasing has to be taken into account. The first half of the extract (from the start to
the third beat of bar 4) consists of two phrases and the second half is one phrase
with a small, but audible rallentando in bar 8. This raises the question of whether
phrasing should be an issue in Examples 5.1 or 5.3 and whether some licence
should be given accordingly. (The poco rall. at the end of bar 12 of Kurze Schatten
II, and the relatively very long gap between the last note of bar 14 and the first
played note in bar 15 would seem to suggest that bars 13 and 14 constitute a
phrase though the music is highly gestural and any notion of phrasing in the
conventional sense would appear to be inappropriate. This will be discussed in
more detail later.) The trill at the beginning of bar 2 and the spread chord at the
beginning of bar 4 (notes 5 and 14 respectively) also have the effect of lengthening
the note value and must be taken into consideration. Table 5.3 shows the timings
of the significant notes.
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Table 5.3 Bach, Bourrée, bars 1–8 – significant notes with actual timings (seconds) Significant notes Actual time (secs)
1 1.4 2 1.92 3 2.352 4 2.562 5 3.125 6 3.85 7 4.06 8 4.325 9 4.81 10 5.275 11 5.76 12 6.2 13 6.67 14 7.05 15 8.075 16 8.43 17 8.98 18 9.88 19 10.77 20 11.66 21 12.525 22 13.04 23 13.25 24 13.52 25 14.0 26 14.49 27 15.05 28 15.525
Even with this example it is not a simple matter to determine the metronome
mark. It is pointless using a bar that contains an ornament or a phrase ending to
calculate the tempo so a comparison of the lengths of bars that do not contain
phrase endings, with each associated implied metronome marking, is shown in
Table 5.4.
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Table 5.4 Bach, Bourrée – bar lengths with implicit mm
Bar number Bar lengths (secs) Implied mm (1/4 = )
1 1.725 139.13
3 1.775 135.21
5 1.79 134.08
6 1.755 136.75
7 1.965 -‐
Bar 7 contains a rallentando towards the cadence so again is not useful for the
calculation of the metric. Table 5.5 shows the comparison of the actual and
theoretical timings of the twenty-‐eight notes. Notes 1 to 8 are in the first phrase so
calculated with mm = 139.13 (quarter note) which corresponds to the bar length of
1.725 seconds. Notes 9 to 15 in the second phrase are calculated with mm = 135.21
and notes 16 to 28 in the last phrase are calculated using mm = 135.415 – the
average of the implied metronome markings of bars 5 and 6. The theoretical times
have been rounded up to two decimal points.
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Table 5.5 Bach, Bourrée, bars 1-‐8 – actual and theoretical timings of the
significant notes (colour coded for each phrase)
Note Actual timing (secs)
Theoretical timing (secs)
Difference (minus means
late)
Comments
1 1.4 1.4 0 By construction
2 1.92 1.83 -‐0.09
3 2.352 2.26 -‐0.092
4 2.562 2.69 0.128
5 3.125 3.13 0.005
6 3.85 3.56 -‐0.29
7 4.06 3.77 -‐0.29
8 4.325 3.99 -‐0.335
9 4.81 4.83 0.02
10 5.28 5.28 0 By construction
11 5.76 5.72 -‐0.04
12 6.2 6.16 -‐0.04
13 6.67 6.61 -‐0.06
14 7.05 7.05 0 By construction
15 8.075 7.94 -‐0.135
16 8.43 8.54 0.11
17 8.98 8.98 0 By construction
18 9.88 9.86 -‐0.02
19 10.77 10.74 -‐0.03
20 11.66 11.62 -‐0.04
21 12.525 12.5 -‐0.025
22 13.04 12.94 -‐0.1
23 13.25 13.16 -‐0.09
24 13.52 13.38 -‐0.14
25 14.0 13.82 -‐0.18
26 14.49 14.26 -‐0.23
27 15.05 14.7 -‐0.35
28 15.535 15.14 -‐0.395
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The notes 9 and 16 correspond to the anacrusis and have therefore been calculated
backwards from the successor note using the appropriate new metronome mark. It
is readily seen that the differences are mostly of a very small order – usually less
than 0.1 seconds. The discrepancies towards the end of the example are a measure
of the rallentando. Very small discrepancies are due to the restriction of the
numbers to two decimal places.
Overall the analysis seems to show a high degree of rhythmic precision, even
allowing for expression. A possible objection to this methodology is that by taking
three different metronome marks the calculations have been made to fit the
original observations. The problem is that any ‘classical’ piece of music will be
phrased and played with appropriate interpretation and some flexibility in tempo
is to be expected – especially in a piece for a solo instrument. The three different
metronome settings however correspond to quarter note lengths of 0.43125,
0.44375 and 0.44308 seconds respectively so it is reasonable to credit Williams
with retaining an accurate pulse throughout. It is clear also that no piece, played
with any expression at all, will be metronomically accurate over a long period of
time. At some point though it must be reasonable to look for a degree of rhythmic
accuracy and if this cannot be achieved in one or two bars within a putative phrase
then the question of the composer’s use of such complex rhythms, such as is seen
in the examples given earlier, remains.
5.5 Analysis of Stockhausen -‐ Klavierstücke 1
Thomas’s analysis of bar 6 of Stockhausen’s Klavierstücke 1 was given in the last
chapter. He recalculated the tempos to avoid the complex notation arriving at mm
8th = 98.4 and mm 8th = 103.123 respectively for the two groups (assuming an
initial mm 8th = 90). For ease of reference the example is given again here
(Example 5.10).
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Example 5.10 Stockhausen, Klavierstücke 1, bars 4-‐6
As Thomas rightly points out it is what performers actually do that needs
investigation. The following is one answer to this question.
Taking as an example the recorded performance by Steffen Schleiermacher
(Schleiermacher 2000) and using Audacity to analyse the waveform of bars 5 and
6, the tempo he has used must first be found. The following table (Table 5.6) gives
the start times of bars 5, 6 and 7 and the start times of the two groups in bar 6
(estimated to two decimal places)
Table 5.6 Stockhausen, Klavierstücke 1 – starting times of bars 5-‐7
Start time (secs)
Bar 5 19.16
Bar 6 -‐ start of group 1 21.02
Bar 6 – start of group 2 22.46
Bar 7 24.03
From this it follows that bar 5 is 1.87 seconds and bar 6 is 3.01 seconds. This gives
each 8th in bar 5 to be 0.47 seconds or mm 8th = c128. For bar 6, each 8th is 0.75
115
seconds or mm 8th = 80 so it is not clear what tempo Schleiermacher had in mind
for these two bars.
Taking bar 6 (and thus a mm 8th = 80) the first group of two 8ths should take 1.20
seconds and the second group of three 8ths should take 1.81 seconds. The
waveform shows group 1 = 1.44 seconds and group 2 = 1.77 seconds10.
Schleiermacher therefore takes 0.24 seconds longer for the first group and is 0.04
seconds shorter for the second. This seems to show a degree of accuracy of his
subdivision of the bar into 5 equal parts and distribution of the notes between
them. On the other hand it is easy to hear that Schleiermacher does not divide the
first group into seven equal parts as a distinct pause can be heard between the 5th
and 6th notes in this group.
Recall that for Thomas, these tempo shifts ensure the performer is ‘kept
sufficiently alert’ (Thomas 2009, 84) and support his argument that the performer
must ‘adopt an approach which focuses on ‘action’ rather than ‘interpretation’
(Thomas 2009, 85). Is it possible, on the evidence of the recording alone, to tell if
Schleiermacher was adopting such an approach? The score obviously prompted
him to perform it the way he did but to what extent did interpretation play a part?
Can the two ever really be separated?
It is of interest to note that Thomas chose exactly the same bar of Stockhausen as
Marsh (Marsh 1994, 85). Marsh states it is one of the examples given by the
linguist Nicolas Ruwet in an article published in 1958 (Marsh 1994, 85). According
to Marsh, Ruwet’s point was that, with such inaccurate performances, such
complexity was no more than conceptual. This of course is exactly the criticism
made against new complexity.
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5.6 Irvine Arditti’s performance of Ferneyhough’s INTERMEDIO alla ciaccona – a
reconsideration of Marsh’s analysis
The next analysis is of Irvine Arditti’s recording) of Ferneyhough’s INTERMEDIO
alla ciaccona for solo violin11. The results can then be compared with Marsh’s
analysis of the same excerpt. In the interview with Paul Archbold, Arditti states
that he was given the last two pages of the score two days before the first
performance and that his recording was made the day before the concert – that is,
one day after receiving the score (Arditti 2012). It is not known if this is the
recording that was subsequently given a commercial release.
Marsh analysed the first four bars but the first six seem to constitute a phrase (or
perhaps two). It is easier to calculate a metric if the sixth bar is included as there is
a clear start to that bar. Example 5.11 is the relevant part of the score and Example
5.12 the schematic view of the same with the significant notes labelled. As there
are so few notes actually bowed (as opposed to sustained) all the played notes are
significant.
Example 5.11 Ferneyhough, INTERMEDIO alla ciaccona, bars 1-‐5
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Example 5.12 Ferneyhough, INTERMEDIO alla ciaccona – schematic view of
bars 1-‐5
Table 5.7 gives the usual data. This time all measurements have been restricted to
two decimal places.
Table 5.7 Ferneyhough, INTERMEDIO alla ciaccona, bars 1-‐6 – actual and
theoretical timings
Note Actual time (secs) Theoretical time
(secs) Difference (minus
means late) Comments
1 1.0 1.0 0 by construction
2 6.68 6.21 -‐0.47
3 7.35 6.49 -‐0.86
4 12.83 14.77 1.94
5 16.71 16.2 -‐0.51
6 17.66 17.1 -‐0.56
7 18.7 18.71 0.01
8 19.42 19.63 0.21
9 20.19 20.2 0.01 by construction
The twenty-‐four 8th notes are played in 19.19 seconds which corresponds to an 8th
note duration of 0.8 seconds (actually 0.79958333 seconds) and a metronome
mark of 8th = 75. This is a fair bit faster than the composers tempo indication of 8th
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= 54-‐60. The 0.01 of a second discrepancy at note 9 is due to the calculations being
restricted to two decimal points.
Pace Roger Marsh, this analysis does not show such an inaccurate performance if
strict adherence to Ferneyhough’s rhythmic schema is the sole criterion. The
glaring exception is note 4 which is a shade under two seconds adrift but all but
one of the other notes are about 0.5 or less of a second off the theoretical time. And
this is over a total period of about twenty seconds. Speculations about reasons for
this inaccuracy in note 4 are reserved until section 5.10. Marsh states
‘Ferneyhough’s performance note allows for some flexibility in the basic tempo,
but does insist that the tempo should remain constant throughout’ (Marsh 1994,
84). This imperative to keep the tempo constant does not appear in the published
score. The notes on the CD state that Ferneyhough was the artistic advisor to the
recording project so one can only assume he was satisfied with the performance.
There is however, yet another way of interpreting this same data. In previous
examples we have restricted analysis to one or two bars and if we take bar 5 in
isolation we get the following Table 5.8. The tempo is now 8th note = 86.21. Overall
the notes could be said to “fit” better but it is ironic that the one note that is part of
a complex subdivision in this bar (note 8) could be considered to be the one less
accurately played.
Table 5.8 Ferneyhough, INTERMEDIO alla ciaccona – timings for bar 5-‐6
Note Actual time (secs) Theoretical time (secs)
Difference (minus means late)
Comments
5 16.71 16.71 0 By construction
6 17.66 17.5 -‐0.16
7 18.7 18.9 0.02
8 19.42 19.69 0.27
9 20.19 20.2 0.01 by construction
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This example shows that analysis of performance is not possible purely on the
basis of the recorded result. The artist’s intentions are unlikely to be spelt out and
a thoroughly metronomic performance would probably be heard as sterile in this
music as in the music of Bach. Alternatively one might argue that if the performer
can’t ‘get it right’ in relatively easy passages (in comparison with the frenetic
activity for much of the rest of this particular score) why should we take seriously
their insistence that they have made detailed analyses of the rhythms? It must be
added at this point that, apart from his short essay in Complexity? (Arditti 1990, 9)
it is not known if Arditti has made such a claim. Marsh makes a similar point when
he says:
It may be argued that fluctuations in tempo, however dramatic, do not
substantially change the nature or ‘meaning’ of the music and I would of
course accept that. There are occasions, however, when performer
rationalisation (for it is this and not sloppiness which accounts for the
discrepancies noted above) does appear to come perilously close to
changing the music into something the composer almost certainly did
not intend or predict. (Marsh 1994, 84)
Marsh gives his own transcription of Arditti’s performance of the first four bars
(Marsh 1994, 84 Ex. 3), which he construes as three bars. The nested ‘irrationals’
of bars 2 and 4 of the original are replaced by nothing more complicated than a
triplet. He gives another transcription of the first two bars of the fifth system on
the first page (page 2 of the score) that contains none of Ferneyhough’s complex
rhythms (Marsh 1994, 84 Ex. 5). Whilst these transcriptions may be accurate this
really only prompts the following question: if Ferneyhough had written in such a
way would Arditti’s performance be any more rhythmically accurate to this new
scoring? It is probable that Arditti would have ‘interpreted’ this notation – perhaps
to the point where it might have resembled Ferneyhough’s original. These ideas
will be considered in more detail in Chapter Ten.
120
Marsh’s concern is whether new complexity can become a ‘coherent musical
language’ (Marsh 1994, 85). He concludes that:
this is music in which precise detail is, paradoxically, of little
importance. It is a music of generalised, if often spectacular, effect. It is
not a music concerned with organic continuity or evolution, except in
theoretical terms. (Marsh 1994, 86)
This is a serious criticism. One might also add that whilst all the analyses have
been focussing on assessing the rhythmic accuracy, further investigation might be
made as to the accuracy of the other musical parameters – in particular the
quartertone pitches.
5.7 Bone Alphabet – Schick and Tomlinson
The next two analyses are of the same piece. There are (at least) two commercially
available recordings of Ferneyhough’s Bone Alphabet for percussion; one by the
dedicatee Steve Schick (Schick 2000) and the other by Vanessa Tomlinson (Elision
1998). Example 5.13 (see the supplementary files for the first page, of Bone
Alphabet) is the first 5 bars of the score with the significant notes numbered. There
is no need for a schematic view here. Before looking closely at the timings it is
worth mentioning some of the difficulties encountered when looking to the
waveform and trying to tie it to what is heard so that significant notes could be
chosen. This piece is unusual in that Ferneyhough has left it to the performer to
decide what percussion instruments to use. The two performers made different
choices. Helpfully Schick gives his instrumentation (Schick 1994, 135) but there is
no information about Tomlinson’s choice. The first bar was the best choice for
identifying the high woodblock and low tom tom in Schick’s performance and it
was then easy to identify the sound, if not the actual instrument, that Tomlinson
used. A percussionist would probably be able to differentiate between the sounds
121
of the different instruments but for the non-‐specialist it is difficult to distinguish
them in the complex texture of this score. Note 3 has been included as it appears
that Schick plays it on the high wood block – the tone is identical to notes 1 and 2 –
whereas in Tomlinson’s recording it is definitely a different sound. It is not known
why Schick changed this (if indeed he did) but it is confusing in what is a difficult
score to follow (again, for the non–specialist).
Example 5.13 Ferneyhough, Bone Alphabet, bars 1-‐5 (with significant notes
numbered)
As has already been mentioned several times, Schick is quite explicit that he learnt
this piece in a bar by bar fashion. His three ways to approach learning the rhythms
have already been summarised in Chapter Four. One would expect a synthesis
when putting it all together and finally recording it, but this recording does seem
to retain some element of this fragmented learning approach. This can be seen by
calculating the metronome marks for each of the first four bars. Table 5.9 shows
the bar lengths and corresponding metronome marks from the performance by
Schick and Table 5.10 the same for Tomlinson. The start of bar 3 was particularly
difficult to assertain as the pianissimo notes were all but invisible on the waveform.
Using notes 17 and 19 in Tomlinsons performance a calculation was made to
122
determine the start of bar 3. This produced a predicted time of 8.038 seconds
which corresponds quite well with the aurally and visually perceived note 16. A
forward calculation using bar 2 (that is, notes 9 and 17) resulted however, in the
determination of the start of bar 3 to be some way before several of the notes at
the end of bar 2. This was therefore rejected. Again, this illustrates the problems
encountered in this methodology.
Table 5.9 Ferneyhough, Bone Alphabet, bars 1-‐4 – timing data and implied mm
(Schick) Bar Bar Length (secs) Implied mm (8th)
1 3.525 68.18
2 2.5 48
3 4.85 61.86
4 7.5 56
Table 5.10 Ferneyhough, Bone Alphabet, bars 1-‐4 – timing data and implied mm
(Tomlinson) Bar Length (secs) Implied mm (8th) 1 4.1 52.54
2 3 40
3 5.92 50.68
4 7.43 56.53
At this point we draw attention to the composer’s tempo of 8th note = 54 and the
rigoroso which could be construed as referring to tempo. Note that both
performers drop the tempo substantially for bar 2. One can speculate that the
difficulties in performing this bar were such that it was only feasible at a slower
tempo, though this reason would not be acceptable in more traditional areas of
music. This could be another indication of the residue in performance of the bar by
bar learning process. The piece does seem, however, to have been composed in
some sort of modular fashion with many (if not most) bars exhibiting some
123
repetitive rhythmic patterning. This could be contrasted with Examples 5.1, 5.3
and 5.11 where no such patterning can be perceived.
Tables 5.11 and 5.12 show, for each performer, the usual table of timings of the 26
significant notes together with the theoretical timings calculated according to the
metronome marks given in Table 5.9. The colours indicate each of the four bars.
Table 5.11 Ferneyhough, Bone Alphabet – timing data from Schick’s performance
of bars 1-‐4
Note Actual time (secs) Theoretical time (secs)
Difference (minus means late) Comments
1 0.225 0.225 0 by construction
2 0.75 0.665 -‐0.085 3 1.25 1.215 -‐0.035 4 1.44 1.413 -‐0.027 5 1.7 1.545 -‐0.155 6 2.14 1.985 -‐0.155 7 2.74 2.49 -‐0.25 8 3.035 2.975 -‐0.06 9 3.75 3.75 0 by construction
10 4.2 3.805 -‐0.395
11 4.85 4.215 -‐0.635
12 4.85 4.792 -‐0.058
13 5.4 5.208 -‐0.192
14 5.8 5.625 -‐0.175
15 5.45 5.664 0.214
16 6.25 6.25 0 by construction
17 6.85 6.943 0.093
18 8.5 8.675 0.175
19 11.1 11.1 0 by construction
20 11.43 12.07 0.64
21 12.69 12.555 -‐0.135
22 13.15 13.04 -‐0.11
23 14.33 14.01 -‐0.32
24 15.35 14.98 -‐0.37
25 15.95 15.465 -‐0.485
26 16.71 15.95 -‐0.76
27 17.55 16.92 -‐0.63
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By comparison with the examples looked at so far, and with the proviso that the
metronome marks are as calculated, these figures show a remarkable degree of
rhythmic precision. Of the twenty-‐seven notes considered, only three notes are
more than half a second out and thirteen less than 0.2 seconds. Notes 11 and 12
were indistinguishable on the waveform and only becoming so at a very high
resolution where they were accordingly recorded as being at the very same time.
Table 5.12 Ferneyhough, Bone Alphabet – timing data from Tomlinson’s
performance of bars 1-‐4
Note Actual time (secs) Theoretical time (secs)
Difference (minus means late) Comments
1 1.05 1.05 0 by construction
2 1.6 1.563 -‐0.037 3 1.97 2.075 0.105 4 2.07 2.434 0.364 5 2.55 2.588 0.038 6 3.06 3.1 0.040 7 3.6 3.664 0.064 8 4.3 4.253 -‐0.047 9 5.15 5.15 0 by construction
10 5.92 5.806 -‐0.114
11 6.49 6.298 -‐0.192
12 6.53 6.4 -‐0.13
13 7.09 6.9 -‐0.19
14 7.57 7.4 -‐0.17
15 7.57 7.447 -‐0.123
16 8.15 8.15 0 by construction
17 8.92 8.996 0.076
18 11 11 0
19 14.07 14.07 0 by construction
20 14.64 15.081 0.441
21 15.73 15.662 -‐0.068
22 16.32 16.142 -‐0.178
23 17.39 17.254 -‐0.136
24 17.6 18.266 0.666
25 18.85 18.846 -‐0.004
26 19.3 19.327 0.027
27 20.35 20.439 0.089
125
If anything Tomlinson’s account exhibits an even greater degree of rhythmic
accuracy. The exception, almost unaccountably, is note 24 which should come
exactly on the fifth 8th note of a 7/8 bar.
5.8 Ferneyhough, Bone Alphabet, bars 20-‐22. Schick’s performances
Schick also gives a detailed description of his approach to learning the triplet
motive that occurs five times in bars 20-‐22 of Bone Alphabet (Example 5.14)
(Schick 1994, 141-‐3, Schick 2006, 108-‐9). (See also the supplementary files for
page 6 of the score – bars 15-‐22.)
Example 5.14 Ferneyhough, Bone Alphabet, bars 18 -‐22
He writes:
Reconfiguring the nested polyrhythms as changes in tempo supports
the sense of fractured time inherent in this passage. An accurate
performance of this material should stutter: it sound, feel, and look
interrupted and incomplete (Schick 2006, 108)
126
After giving the analysis he calculates the tempi of each appearance of the figure as
mm = 60, 52.5, 75, 44 and 79. It is then that he makes his comment about being
able to remember and reproduce such tempi quoted earlier (Schick 2006, 109).
As Schick has asserted that such finely delineated rhythms can be reproduced
accurately it is reasonable to analyse his recording (Schick 2000) to see if this can
be verified objectively. To this end the passage was analysed using the Audacity
wave editor. The timings of first notes of each bar were logged together with the
timings of the first and last notes of the first, second, fourth and fifth appearance of
the triplet figure. The third was not easy to assess so was omitted but a reasonable
assessment of accuracy can be made with information about four of the five
instances. The times were estimated to the nearest 100th of a second.
The following (Table 5.13) gives these timings together with the resulting
calculation of the actual tempi for each bar. The start of bar 23 is a rest so the
duration of bar 22 is not easy to determine but it is reasonable to assume the
tempo does not change significantly12.
Table 5.13 Ferneyhough, Bone Alphabet, bars 20-‐22 – timings with implied mm
Bar number Start time Resultant mm (8th)
20 1:34.20 57.97
21 1:38.34 58.37
22 1:43.48 Not calculated.
The next table (Table 5.14) gives the time places of the first and last notes of the
first, second, fourth and fifth triplet figures together with their durations.
127
Table 5.14 Ferneyhough, Bone Alphabet, bars 20-‐22 – timings of 1st and 3rd notes
of triplets
Triplet figure
Time of 1st note (min:secs)
Time of 3rd note (min:secs)
Duration (secs)
1 1:34.20 1:34.88 0.68
2 1:36.33 1:37.16 0.83
4 1:41.08 1:42.02 0.94
5 1:43.92 1:44.70 0.78
The duration does not of course mean the duration of the triplet, merely the
duration of 2/3rds of the triplet, as the precise end of the figure (that is the actual
duration of the third note) is impossible to determine. These durations therefore
need to be increased by a factor of 3/2 to represent the duration of the triplet as a
totality.
It is therefore reasonable to take Schick’s triplets as having the durations shown in
Table 5.15.
Table 5.15 Ferneyhough, Bone Alphabet, bars 20-‐22 – inferred lengths of triplets
Triplet figure Total duration (secs)
1 1.02
2 1.25
4 1.41
5 1.17
If we use Schick’s 8th note pulse for each bar (8th = 1.035 seconds for bar 20 and
1.028 seconds for bar 21 and 22) the triplet figures should have the durations
listed in Table 5.1613.
128
Table 5.16 Ferneyhough, Bone Alphabet – theoretical lengths of triplets in bars 20-‐
22 implied by Schick’s tempi
Triplet figure Duration (secs)
1 1.035
2 1.18
4 1.26
5 0.78
From which we conclude that Schick deviates from his own tempi by the durations
shown in Table 5.17.
Table 5.17 Ferneyhough, Bone Alphabet -‐ triplets in bars 20-‐22 -‐ Schick’s deviation
from his own tempi
Triplet figure Schick’s deviation from his own tempo
1 0.015 second too short (1.035-‐1.02)
2 0.07 second too long (1.25-‐1.18)
4 0.15 second too long (1.41-‐ 1.26)
5 0.39 second too long (1.17-‐0.78)
Now assuming Ferneyhough’s mm 8th = 60 these durations should be as per Table
5.18
129
Table 5.18 Ferneyhough, Bone Alphabet – triplets in bars 20-‐22 – theoretical
timings based on 8th = 60
Triplet figure Total duration at Ferneyhough’s 8th = 60 (secs)
1 1.0
2 1.14
4 1.23
5 0.76
Schick’s real time deviations from a strict adherence to Ferneyhough’s tempo are
given in Table 5.19.
Table 5.19 Ferneyhough, Bone Alphabet – Schick’s performance compared to
Ferneyhough’s tempo
Triplet Figure Schick’s deviation from 8th = 60 (secs)
1 0.02 too long (1.02-‐1.00)
2 0.11 too long (1.25-‐1.14)
4 0.18 too long (1.41-‐1.23)
5 0.41 too long (1.17-‐0.76)
The above is one way to analyse the accuracy of Schick’s performance. The passage
is a tempo (though comodo) and the relevant notes are reasonably easy to hear and
assess their time values to 100th of a second (using the wave editor). Apart from
the first triplet figure (which corresponds to the beginning of the bar) the placing
of the triplet in the bar has not been assessed for accuracy – only its duration. The
placement of every other note in the three bars also contributes to assessment of
the total, literal accuracy, as do the dynamics and other similar interpretive
aspects.
130
Notwithstanding all these factors it is clear that Schick is less than 0.4 of a second
away from complete rhythmic accuracy, as far as duration of the triplets is
concerned, using his own tempi and less than about 0.4 of a second from
Ferneyhough’s given tempo. Most of the differences are less than 0.2 of a second.
The largest difference is in the last triplet which is still less than 0.4 seconds.
One view is that these differences are irrelevant to the musical experience for the
listener and that the value of such an analysis is nugatory. This would clearly be
the case if Schick had not been so keen to subscribe to the notion of the possibility
of complete accuracy. At 8th note = 60, tenths of a second are easily perceptible. For
example, each 32nd note at this tempo would be take 0.25 seconds and the
recognition of accuracy of subdividing a note value at this tempo in to four equal
parts is fairly rudimentary.
5.9 Dillon’s Shrouded Mirrors, Grahame Klippel’s performance
Of the three case studies recorded by me, the only piece with notation comparable
in its complexity to the previous examples is Dillon’s Shrouded Mirrors (see
Chapter Nine and the supplementary data file). The following analysis is of the
first six bars of my performance. Whilst the composer has indicated mm 8th = 72
for the duration of this portion, on analysis my mm was determined to be
somewhere between 53 and 58. This excerpt is comparable with the earlier
examples: in particular, the regular pulse means the results of the analysis can be
compared with the analysis of the Bach Bourrée.
In order to calculate the duration of the whole section the placement of the first
chord of bar 7 has to be ascertained. As bar 7 starts with a rasgueado chord it is a
matter of judgment as to where the beat actually falls. The error factor here is
negligible though when averaging over the whole length of the passage.
131
Example 5.15 shows the relevant extract. Unlike the other examples, the time
placements of almost all the distinct notes have been calculated. That is, most of
the notes have been deemed to be significant. This example can therefore be
analysed in more detail than the others.
Example 5.15 Dillon, Shrouded Mirrors, bars 1–7
Example 5.16 gives the usual schematic view with the significant notes numbered.
Example 5.16 Dillon, Shrouded Mirrors, bars 1-‐7 -‐ schematic with significant notes
The following table gives the timings for the 49 notes.
132
Table 5.20 Dillon, Shrouded Mirrors, bars 1-‐7 -‐ actual timings for significant notes
Note
Actual time (secs)
Note
Actual time (secs)
1 2.57 26 11.45 2 2.91 27 11.73 3 3.18 28 11.93 4 3.61 29 12.26 5 3.77 30 12.36 6 4.08 31 12.90 7 4.38 32 13.24 8 4.51 33 13.32 9 4.67 34 13.96 10 5.27 35 14.44 11 6.4 36 14.69 12 6.57 37 15.08 13 7.1 38 15.35 14 7.21 39 15.88 15 7.57 40 16.00 16 7.97 41 16.41 17 8.08 42 16.58 18 8.37 43 16.71 19 8.70 44 17.03 20 8.88 45 17.39 21 9.57 46 17.62 22 9.97 47 17.86 23 10.52 48 18.26 24 10.70 49 18.83 25 11.07
For the first analysis of the accuracy of the rhythmic figures it is clear that, as the
times of notes 1, 4 and 9 are known, it is possible to assess the accuracy of the
subdivisions of the first two beats.
The length of the first beat is 3.61 -‐ 2.57 = 1.04 seconds. This corresponds to mm
8th = 58. The length of the second beat is 4.67 – 3.61 = 1.06 seconds. This
corresponds to mm 8th = 57. (The calculations for the mm are of course rounded to
the nearest integer.)
133
Table 5.21 gives the theoretical and actual timings for the first beat calculated on
the basis of the beat being 1.04 seconds long.
Table 5.21 Dillon, Shrouded Mirrors, bar 1 – timings for the first beat
Note Actual time (secs) Theoretical time (secs)
Difference (minus means late) Comments
1 2.57 2.57 0 by construction 2 2.91 2.83 -0.08 3 3.18 2.99 -0.19
Table 5.22 gives the same information for the second beat calculated on the basis
of the beat being 1.06 seconds long.
Table 5.22 Dillon, Shrouded Mirrors, bar 1 – timings for the second beat
Note Actual time (secs) Theoretical time (secs)
Difference (minus means late) Comments
4 3.61 3.61 0 by construction 5 3.77 3.79 0.02 6 4.08 4.14 0.06 7 4.38 4.41 0.03 8 4.51 4.46 -0.05
Using this method to analyse rhythmic accuracy, the above tables show that, based
on a very limited time scale, the ‘error’ is extremely small. Only one note is over 0.1
of a second away from its theoretical time.
Table 5.23 gives the same formation for bars 3–7 with the beat length (and mm)
calculated as an average from notes 16-‐49. Bar 3 starts at 7.97 seconds and bar 7
starts at 18.86 seconds so this extract is 10.86 seconds long and thus comparable
to the other examples. The 10 beats average at 1.09 seconds corresponding to mm
8th = 56. This is very slightly slower than the values calculated on the basis of the
134
first two beats of bar 1. Table 5.23 was therefore compiled assuming 8th note =
1.09 seconds.
Table 5.23 Dillon, Shrouded Mirrors, bar 3-‐6 – timings for the significant notes 16-‐
49.
Note Actual time (secs) Theoretical time (secs)
Difference (minus means late) Comments
16 7.97 7.97 0 by construction
17 8.08 8.11 0.03 18 8.37 8.24 -0.13 19 8.70 8.52 -0.18 20 8.88 8.79 -0.09 21 9.57 9.61 0.04 22 9.97 9.79 -0.18 23 10.52 10.51 -0.01 24 10.70 11.02 0.32 25 11.07 11.06 -0.01 26 11.45 11.24 -0.21 27 11.73 11.46 -0.27 28 11.93 11.79 -0.14 29 12.26 11.97 -0.29 30 12.36 12.11 -0.25 31 12.90 12.69 -0.21 32 13.24 13.15 -0.09 33 13.32 13.24 -0.08 34 13.96 13.64 -0.32 35 14.44 14.29 -0.15 36 14.69 14.51 -0.18 37 15.08 15.06 -0.02 38 15.35 15.33 -0.02 39 15.88 15.82 -0.06 40 16.00 16.04 0.04 41 16.41 16.47 0.06 42 16.58 16.69 0.11 43 16.71 16.91 0.20 44 17.03 17.24 0.21 45 17.39 17.56 0.17 46 17.62 17.78 0.16 47 17.86 18.22 0.36 48 18.26 18.33 0.07 49 18.83 18.83 0 by construction
135
It is readily seen from these tables that the error in seconds is never greater than
0.36 of a second with about 60% of the note differences being less than 0.1 of a
second. Specifically, 28 of the 47 notes were less than 0.1 of a second away from
their theoretical time. A further 9 notes were between 0.1 and 0.2 seconds away
from the theoretical time, 7 notes were between 0.2 and 0.3 seconds and 2 notes
were over 0.3 seconds away from theoretical time. The readings of first and last
notes were of course discarded.
It should be noted that the predominant ‘complex’ subdivision of each 8th note is
into 5ths. The 8th note durations calculated above, namely 1.04, 1.06 and 1.09 would
therefore be subdivided into 0.208, 0.212 and 0.218 seconds intervals respectively.
It follows that a difference greater than these values between actual and
theoretical time in a suitable rhythmic figure (for example between notes 1 and 3,
4 and 8 and so on) indicates an error in the performance of the quintuple unit.
Bars 3 and 4 have a 3:2 in one part against the quintuplet subdivision of the 8th
notes in the other part. These bars have a greater degree of complexity to the
others. The relevant significant notes here are 21-‐25 and 26-‐33. For bar 3, only
note 24 seems to be much more inaccurately placed than the others. For bar 4
most of the notes seem to be about 0.2 seconds out from their theoretical
placements so this bar is comparatively more inaccurately played.
At this point it must be made clear that, while the piece contained numerous edits,
this portion was unedited.
It is instructive to analyse these figures using yet another method. It can be argued
that it is not so much the actual placement of the notes compared to an inflexible
measure such as theoretical time that is of aesthetic significance, but the
relationships between consecutive notes.
136
Table 5.24 shows the relationships between the notes of the first two beats of bar 1
based on the numbers given in Tables 5.21 and 5.22.
Table 5.24 Dillon, Shrouded Mirrors – actual and theoretical time differences
between pairs of notes in the first two beats of bar 1
Note pairs Actual time difference (secs)
Theoretical time difference (secs)
Difference (minus means too long)
1-2 0.34 0.27 -0.07 2-3 0.27 0.16 -0.11 3-4 0.43 0.62 0.19 4-5 0.16 0.18 0.02 5-6 0.31 0.35 0.04 6-7 0.30 0.27 -0.03 7-8 0.13 0.05 -0.08
And Table 5.25 gives the same information for bars 3-‐6 based on Table 5.23
137
Table 5.25 Dillon, Shrouded Mirrors – actual and theoretical time differences
between pairs of notes of bars 3-‐6
Note pairs Actual time (secs) Theoretical time (secs)
Difference (minus means too long)
16-17 0.11 0.14 0.03 17-18 0.29 0.13 -0.16 18-19 0.33 0.28 -0.05 19-20 0.18 0.27 0.08 20-21 0.69 0.82 0.13 21-22 0.40 0.18 -0.22 22-23 0.55 0.72 0.17 23-24 0.28 0.51 0.23 24-25 0.37 0.04 -0.33 25-26 0.38 0.18 -0.20 26-27 0.28 0.22 -0.06 27-28 0.20 0.33 0.13 28-29 0.33 0.18 -0.15 29-30 0.10 0.14 0.04 30-31 0.54 0.58 0.04 31-32 0.34 0.46 0.12 32-33 0.08 0.09 0.01 33-34 0.64 0.40 -0.24 34-35 0.48 0.65 0.17 35-36 0.25 0.22 -0.03 36-37 0.39 0.55 0.16 37-38 0.27 0.27 0.00 38-39 0.53 0.49 -0.04 39-40 0.12 0.22 0.10 40-41 0.41 0.43 0.02 41-42 0.17 0.22 0.05 42-43 0.13 0.22 0.09 43-44 0.32 0.33 0.01 44-45 0.36 0.32 -0.04 45-46 0.23 0.22 -0.01 46-47 0.24 0.44 0.20 47-48 0.40 0.11 -0.29 48-49 0.57 0.50 0.07
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Combining the results of Tables 5.24 and 5.25 we see that, of the 39 note pairs, 22
were between 0 and 0.1 second adrift, 11 were between 0.1 and 0.2 seconds adrift,
6 between 0.2 and 0.3 seconds adrift and one over 0.3 second.
If we recall that the first analysis showed that, for bar 3, all but note 24 of the
significant notes 21-‐25 were relatively accurately played and for bar 4 notes 26-‐33
were mostly about 0.2 seconds out. Table 5.25 shows, on the face of it
paradoxically, that the note relationships in bar 3 were more inaccurate than those
in bar 4. It can of course be the case that the placements are inaccurate but the
relationships are accurate. It is another instance of how problematic the
measurement of rhythmic accuracy can be.
5.10 Interpretation of the analyses -‐ comparisons and performance factors
In this section the results of each analysis are inspected with the objective of
assessing the degree of rhythmic accuracy and the influence other musical factors
may have on the performance of the rhythmic figures. In some cases it might be
thought presumptuous to speculate on reasons why the performer has not
performed with greater accuracy. This is unfortunately unavoidable if an
interpretation of the research results is to be attempted.
The first analysis was of bars 13-‐14 of Ferneyhough’s Kurze Schatten II. The
results were presented in Table 5.2. The following graph (Figure 5.1) gives an
alternative view of the figures. The origin of the co-‐ordinate axes corresponds to
the time value of 1 minute as the excerpt starts at 1:19 secs.
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Figure 5.1 Ferneyhough, Kurze Schatten 11 – graphical representation of Table 5.2
This graph, produced using an online chart tool14, shows the inadequacies of
graphical representation. It does however show some divergence between the
theoretical and actual times.
It was stated in section 5.4 that phrasing is an issue and the end of a phrase might
be interpreted with a very slight rallentando. This could easily be the case here as
there is a substantial pause between the last note of bar 14 and the first played
note of bar 15. Another highly significant factor is the need to change right hand
articulation frequently and quickly between tasto where the right hand15 plucks
the strings very near or even over the fingerboard, that is towards the centre of the
string, and pizzicato where the palm of the hand is resting very close to, or actually
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on, the bridge of the guitar. There is also the frequent need to interpolate the
harmonics. These demand a very sensitive touch by a left hand finger in exactly the
right position over the fret to avoid getting a noise instead of the bell like tone
intended. In addition to these technical requirements there are also rapid changes
of dynamic and articulation (staccato, vibrato). Again, as mentioned in section 5.4,
the passage has a gestural rather than motoric quality and the performer may not
be prioritising rhythmic precision.
The next analysis was of the first part of the Bach Bourrée. A degree of
interpretation by the performer is expected and can be inferred from the data. The
analysis clearly showed the phrasing. For example, notes 6, 7 and 8 arrived later by
a significant amount compared to the other notes in the phrase. Similarly, notes 26,
27 and 28 indicate the expected rallentando. The timing of note 6 signaled the
effect of the trill in bar 2. The music had little of the gestural content of the
previous example and, as the bourrée is a dance movement, it is understandable
that the performer would prioritise rhythm. Figure 5.2 shows the relationships
graphically. Note the almost complete identity of the theoretical and actual lines.
The data given in the tables clearly gives a more reliable view. The ¼ note duration
was calculated to be about 0.44 seconds for much of the extract so as the music
moved generally in ¼ and 8th notes the deviation from theoretical time (apart from
the phrase endings and ornaments) was extremely small.
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Figure 5.2 Bach, Bourrée – graphical representation of Table 5.5
The next analysis was of bar 6 of Stockhausen’s Klavierstücke 1 (see Example
5.10). This was a very short excerpt (3.01 seconds) so not comparable to the other
examples from the point of view of assessing accuracy over a period of several
bars. However, it did provide the opportunity to see how the performer had
performed a rhythmic figure comparable to some of Ferneyhough’s. The results
showed that the subdivision 5:4 was accurate but that the subdivision of the first
group 7:8 was uneven. The reason for the quite audible gap between the 5th and 6th
notes (the two chords D flat, C natural – E natural, D sharp) of this group might be
the sffz marking on the E natural and the attempt to mark the difference between
the fff of the first 5 notes and the ff on the D sharp of the 6th note group.
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The substantial difference in mm between bars 5 and 6 is puzzling. The performer
might have wanted to press on and slightly shorten what might be construed as a
pause, shaping it as the end of a phrase. It is not possible to tell.
The next analysis was of Arditti’s performance of Ferneyhough’s INTERMEDIO alla
ciaccona. This passage is about 20 seconds long so comparable to the other
examples. Figure 5.3 gives the usual information in graphical form.
Figure 5.3 Ferneyhough, INTERMEDIO alla ciaccona – graphical representation of
Table 5.7
This music is gestural in a similar manner to the Kurze Schatten II example given
earlier so the difficulty in detecting or calculating a pulse that conveys
unequivocally the mm chosen makes an analysis of rhythmic accuracy quite
tentative. The ambiguous phrasing possibilities also suggest alternative
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interpretations of the data. As the performance of several of the significant notes
(in particular, notes 7, 8 and 9) do correlate reasonably well with their theoretical
time counterparts, one can only speculate as to why the others do not – by factors
of 0.5 of a second and longer. The timings seem to suggest that Arditti construed
notes 1 and 2 as one phrase, and notes 3 and 4 as another. Slightly elongating the
first phrase would make note 2 slightly late and note 3 even later as an audible
indication of the start of the phrase. Note 4 coming early might then be an
indication of the Arditti’s need to resolve the sustained notes. It seems unlikely
that technical issues, such as the need to prepare for the microtones, would be the
reason for any discrepancy as bars 4 and 5 are relatively accurately played despite
all but one of the chords containing a microtone. When bar 5 was analysed
separately an alternative reading of the rhythmic relationships was obtained that
showed rather greater accuracy. It might be that, as this bar is more clearly
subdivided into five 8th note groups, the subdivisions were more clearly defined.
The prevalence of microtones throughout the whole piece does not support the
earlier hypothesis that these might impose technical restraints.
Several bars from two performances of the first four bars of Ferneyhough’s Bone
Alphabet were then analysed. The duration of this passage was about 20 seconds
and thus comparable to the other examples when an average was taken to
calculate the mm. The music here seems modular with each bar apparently
showing a coherent rhythmic schema unrelated to that of the following bar. Both
recordings showed a high degree of accuracy; small, but potentially significant,
differences are not well represented by these graphical methods.
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Figure 5.4 Ferneyhough, Bone Alphabet (Schick). Graphical representation of
Table 5.11
Figure 5.5 Ferneyhough, Bone Alphabet (Tomlinson). Graphical representation of
Table 5.12
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Both analyses suggest a high degree of rhythmic precision is possible thus
supporting the high modernist view – that rhythm is an independent parameter –
is viable. There seems to be no reason why the other examples could not be played
with comparable rhythmic precision. On the other hand, both performers dropped
the tempo for the second bar. These analyses were also calculated on a different
mm for each bar.
It really isn’t possible for a non-‐specialist to comment on what performative
factors might have influenced a percussionist but one can speculate that the rapid
changes of dynamic in each of the first four bars and the necessity to range over 4-‐
6 different percussion instruments might be a factor.
The last analysis was of my own performance of the first six bars of Dillon’s
Shrouded Mirrors. My learning methods will be given later (in the case study) but
suffice it to say my priority, bearing the Tempo giusto in mind, was to maintain a
regular pulse. As this was the first time I have learnt the piece it is likely that, as
Redgate found with Ausgangspunkte, I might refine my interpretation over time. I
was indeed surprised when I found my analysis showed my tempo was rather
slower than indicated. This is despite having heard the other two recorded
versions and using a metronome in the early stages of learning.
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Figure 5.6 Dillon, Shrouded Mirrors. Graphical representation of Table 5.23
The music has a regular 8th note pulse for much of the duration so this excerpt can
be compared to that of the Bach Bourrée. The several analyses showed a degree of
accuracy comparable to the other performances given. There were no egregious
errors for which explanations or speculations need to be contrived. There were no
instrumental issues to influence the performance of the rhythmic figures, the tonal
changes from sul pont to sul tasto being routine for guitarists. It is not possible for
me to comment on the aesthetic qualities of my own performance.
5.11 Conclusions
The premise of this chapter is that it must be possible to assess the outcome of the
methods performers use to analyse, and thus learn, complex rhythms and it is
worth reiterating that the examples for analysis were chosen so that the
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performer’s strategy for dealing with rhythmic figuration could be determined. It is
therefore important to know if different methods produce significantly different
results. Some methods are quite rigorous but do they translate to performances
that are more accurate? Is there an aesthetic dimension to rhythmic accuracy? It
is, however, regrettable that few performers have indicated whether they use any
of the learning methods given above.
This has been neither a representative survey of new complexity pieces nor of new
complexity composers. Neither is it a comprehensive survey of methods of
assessing rhythmic accuracy. Each example shows that there are always choices to
be made about which extract is to be analysed. If just one bar or even one beat is
extracted the corresponding results might be rather different to those obtained by
analysis of a longer section and, in consequence, averaging mm or note length. It is
also the case that the smaller the unit that is analysed the smaller the note
differences are likely to be.
In the analysis of Shrouded Mirrors yet another method was introduced. The
measurement of note relationships showed another way of interpreting the figures
obtained from the waveform. This is of course most useful if most of the notes in
the passage are significant, and hence adjacent. It is not clear what method gives
the best indication of rhythmic accuracy, as the interpretation of the results is
slightly different.
If the relatively minute differences are ignored, we can see that Schick, Tomlinson,
and my own performances display similar degrees of accuracy to the control.
Morris and Arditti seem, at times, rather wayward. The comparisons though may
not be fair; as stated earlier, the first movement of Kurze Schatten II and the
opening of INTERMEDIO alla ciaccona are much more gestural pieces and an artist
may consider the separation of gestural events may be slightly modified for
aesthetic reasons (see (Kanno 2001)). The results also support the view that no
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great abuse to the overall integrity of the work is inflicted if rhythmic accuracy is
not prioritised.
On the other hand, these examples can be interpreted as showing that a high
degree of rhythmic precision is possible should the performer be prepared to take
the time to do the analysis and be able to remember the results over perhaps many
years and performances. A weaker conclusion is that if the performer prioritises
rhythmic precision then a performance that at least adheres to the accurate
placement of the beat, will produce an acceptable result. In the end, the assessment
as to whether or not the overall performance is of sufficient quality to meet the
aesthetic criteria the composer has in mind is imponderable.
The question remains as to what constitutes an acceptable degree of accuracy. On
the face of it a divergence from a strict metronomic pulse by a matter of a few of
hundredths of a second might seem quite an achievement and divergence by
almost 0.5 of a second might be construed as quite inaccurate. Is there musical
‘meaning’ in such rhythmic complexity? If so then this meaning should be
appreciable by the listener – especially as the work enters the repertoire and
becomes familiar. Given that the score is (normally) available to both listener and
performer, should listeners be prepared to applaud inaccurate performances? The
listener might be considered to be colluding with the performer against the
composer by accepting such deviance from the composer’s intentions.
Returning to Marsh’s question of whether or not new complexity is, or can become,
a ‘coherent musical language’ the first question to ask is ‘what is a coherent
musical language’? The performances that have been analysed here all confirm his
belief that the music has a ‘spectacular effect’. On the other hand his qualification
that ‘It is not a music concerned with organic continuity or evolution, except in
theoretical terms’ seems questionable. If the music is composed with some
‘theoretical’ concern for organic continuity and evolution one would expect that to
be appreciable in performance, at least to some degree. The composers mentioned
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previously have, however, all stressed that their music is not determined by
process. The composer is always present making choices. If performances of the
music have an effect they must be more than vapid, meretricious displays of
virtuosity. The performances would not be deemed successful by anybody if they
presented an incoherent musical argument. This music does not follow traditional
modes of musical development and has to be accepted in its own terms.
Notes
1. Irvine Arditti’s performance is on the following CDs:
Irvine Arditti: Recital for Violin Disques Montaigne, WM 334 789003
Brian Ferneyhough: Nieuw Ensemble, Etcetera KTC1070
(Arditti 1990 and Nieuw Ensemble 1989).
A comparison of the timings, as per Table 5.7, of the recordings using
Audacity shows identical times for the significant notes though the
waveforms are not quite the same. They may be two different recordings.
Marsh also compared Arditti’s recording for the BBC’ Music in Our Time in
1993 but found no significant differences in the timings (Marsh 1994, 86).
2 This is not strictly true as a faster piece might contain little detail and a very
slow piece might have a great density of detail but the point is that the
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examples must be chosen so that measurement is possible and comparisons
valid.
3. Morris’s first recording is on (Elision 1998)
4. The numerical data (primarily timings) in this chapter is presented initially in
the form of tables. The significance of the data is explained immediately after
each table and little note has to be taken of the actual numbers. As the whole
point of analysing these timings is to obtain information about accuracy it is
essential to give the raw data. Alternative methods of presenting this data
have been considered and rejected. Graphical representation can actually be
misleading; the choice of scale can make the information ‘fit’ alternative
interpretations. This is explained in section 5.3. Simple graphical
representations of the data do, however, appear later in section 5.8, where
the data is interpreted and comparisons made.
5. It is very easy to make errors in such calculations. The arithmetic here has
been checked several times.
6. Gordon Downie: piano piece 2, self-‐published.
7. For example: ‘dialogue and lip movements in a film can be 50-‐60 milliseconds
out of sync before you notice it’ (Brooks 2012).
8. CD. John Williams: Guitar Recital, London 452 173-‐2 but originally released
on LP Delysé ECB3149.
9. The edition used is: J.S. Bach: Cello Suite No. 3 arranged for guitar by John W.
Duarte, Schott GA 214.
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10. Bar 6 is 3.01 seconds long. Divided into 5 8th notes, each 8th note = 0.602
seconds. Therefore the first group of two 8th notes should take 1.204 seconds
and the second group 1.806 seconds.
11. Brian Ferneyhough: INTERMEDIO alla ciaccona, Edition Peters No. 7346. See
note 1 for the recording details.
12. For each triplet figure in turn: Bar 20 is in 4/8 with a duration of 4.14
seconds which implies the 8th note = 1.035 seconds. Bar 21 is in 5/8 with a
duration of 5.14 seconds implying 8th note = 1.028 seconds.
13. 1 should last one 8th note so = 1.035.
2 should last 4/7ths of (2 * 1.035) = 1.18
4 should last 4/7ths of 6/7ths of 5/6ths of (3 * 1.028) = 1.26
5 should last 4/7ths of 2/3rds of (2 * 1.028) = 0.78
14. www.onlinecharttool.com
15. We are assuming the performer is right handed and therefore plucking the
strings with his right hand.
